Call or order online. Reviews The authors It is a must-have for any researcher in the field. Devaney, Mathematical Intelligencer A comprehensive exposition. Seemingly every topic is covered in depth.
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Call or order online. Reviews The authors It is a must-have for any researcher in the field. Devaney, Mathematical Intelligencer A comprehensive exposition. Seemingly every topic is covered in depth. Richey, American Mathematical Monthly The book Ruelle, Ergodic Theory and Dynamical Systems The treatment of hyperbolic systems, including their ergodic properties It is the most accessible treatment of this theory. Takens, Bulletin of the American Mathematical Society Of the current flood of books on the subject, this one distinguishes itself in many ways I recommend it also as an important source to all those involved in the interface between the mathematical theory and its increasingly pervasive role in the scientific world.
It is indispensable for anybody working on dynamical systems in almost any context, and even experts will find interesting new proofs and historical references throughout the book. There are hints and answers provided for a good percentage of the problems in the book.
The problems range from fairly straightforward ones to results that I remember reading in research papers over the last years I recommend the text as an exceptional reference. Haslach, Applied Mechanics Review The book is a pleasure to read. Amiran, Mathematical Reviews The table of contents and preface can be read here.
Some corrigenda are available, including a major correction on page ff. Please report any errors you notice in the book to. Note one serious omission: The first three print runs up to the first paperback printing fail to acknowledge that Section Our sincere apologies for this failure to give due credit.
The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics.
Its concepts, methods and paradigms greatly stimulate research in many sciences and gave rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory.
This book provides the first self-contained coherent comprehensive exposition of the theory of dynamical systems as a core mathematical discipline while providing researchers interested in applications with fundamental tools and paradigms.
It introduces and rigorously develops the central concepts and methods in dynamical systems in a hands-on fashion. It starts with a comprehensive discussion of a series of elementary but fundamental examples. These are used to formulate the general program of the study of asymptotic properties as well as to introduce the principal notions differentiable and topological equivalence, moduli, asymptotic orbit growth, entropies, ergodicity, etc. The main theme of the second part is the interplay between local analysis near individual e.
This is achieved by exploring hyperbolicity, transversality, global topological invariants, and variational methods. The methods include study of stable and unstable manifolds, bifurcations, index and degree, and construction of orbits as minima and minimaxes of action functionals. In the third and fourth part the general program is carried out for low-dimensional and hyperbolic dynamical systems which are particularly amenable to such analysis.
In addition these systems have interesting particular properties. This book provides a large number of systematic exercises in order to be the principal source for the professional training of future researchers. On the other hand the book may be used by advanced undergraduates in mathematics, graduate students in any area of the mathematical sciences and graduate students in science and engineering with a strong mathematical background as well as researchers in any area of mathematics, science or engineering.
Since a considerable part of the material of the book is either previously unpublished or presented in an essentially new way it is also of interest to experts in dynamical systems. Each of the four parts of the book can be the base of a course roughly at the second year graduate level. They are accessible to students having taken standard US first year courses in analysis, geometry and topology.
In fact, the background material beyond multivariable calculus and linear algebra and ordinary differential equations is covered in appendices. This allows to use certain parts of the book, especially parts 1 and 3, as the basis for more elementary courses starting from advanced undergraduate junior or senior level.
Many courses dedicated to more specialized topics can be tailored from this book, such as variational methods in classical mechanics, hyperbolic dynamical systems, twist maps and applications, introduction to ergodic theory and smooth ergodic theory, the mathematical theory of entropy. In the US any university with a graduate program as well as good undergraduate institutions would be able to thus use the book. In continental Europe the book is appropriate for courses to students at any level above undergraduate, as well as to undergraduate students specializing in mathematics.
This book has been used for courses at institutions world-wide. It is among the 50 most cited mathematics books, and virtually every 21st-century PhD in dynamical systems has been trained using it.
Handbook of dynamical systems
His next result was the theory of monotone or Kakutani equivalence, which is based on a generalization of the concept of time-change in flows. His field of research was the theory of dynamical systdms. In he emigrated to the USA. Views Read Edit View history. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbits structure.